Chelsea had appeared to be heading into the quarter-finals, thanks to a 19th minute strike from Timo Werner.
But Erik Lamela forced a shootout with an equaliser in the 83rd minute, finishing from close range after controlling a cross from debutant Sergio Reguilon.
In the shootout, Chelsea’s Mason Mount struck the post to miss the decisive fifth penalty kick after every other penalty kick had been converted.
Chelsea’s new goalkeeper Edouard Mendy had a confident display in his first game since switching from Stade Rennes.
He made a good save to keep out a vicious shot from Spurs’ Spanish left-back Reguilon in the second half.
But Mendy was finally beaten in the 83rd minute, when Reguilon turned in the box and found Lamela.
He controlled the ball at the far post before netting from close range to force the shootout in which Tottenham prevailed.
The victory was revenge for Spurs for a 2019 League Cup semi-final second leg defeat to Chelsea on penalty kicks.
Spurs boss Jose Mourinho, meanwhile, got one over his former Chelsea player Frank Lampard.
“We were ready to fight. I told the players before the penalty kicks that they were magnificent in the second half. We made Chelsea look ordinary. The team waited for the right moment,” Mourinho said.
The League Cup fixture, which came only two days after their 1-1 draw with Newcastle United, was the second game of a gruelling run of four matches in eight days for Spurs.
Mourinho’s side face Maccabi Haifa at home in a Europa League playoff on Thursday before a league fixture at Manchester United on Sunday.
Mourinho made nine changes to the team who had faced Newcastle, sticking with first-choice goalkeeper Hugo Lloris instead of new signing Joe Hart.
He gave a second start in three days to Eric Dier, who stepped up to score the first penalty kick.
“I have to think about three games at the same time. But the players only thought about this game, they were phenomenal. Phenomenal,” added Mourinho, just as he praised England international Dier who left the pitch to go to the toilet during the second half.
“What happened to Eric Dier is not normal, I have to praise him in a special way. It should be forbidden for a player to play two games in 48 hours at this level. What he did is not human to do.”(Reuters/NAN)